Sample paper · GCSE Higher · grades 4–9

GCSE Higher sample Paper 2 (calculator)

The real Paper 2 is 1.5 hour 30 minutes and 80 marks, calculator, and all three papers carry equal weight. This sample is 20 original questions in the same content proportions as the Higher qualification — number 15%, algebra 30%, ratio, proportion and rates of change 20%, geometry and measures 20%, probability 7.5%, statistics 7.5% — with a calculator allowed. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.

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GCSE Higher sample Paper 2 (calculator)

Maths · GCSE Higher · Paper 2 · Calculator · 20 questions

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1.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.
(a)1 × 10³
(b)2.5 × 10⁻⁶
(c)2.5 × 10⁶
(d)2.5 × 10²
2.Solve x² + 7x = 0.
(a)x = 0 or x = 7
(b)x = 0 or x = −14
(c)x = 0 or x = −7
(d)x = −7
3.A box holds 60 crayons. 25 of the crayons are broken and the rest are unbroken. Write the number of unbroken crayons as a fraction of the number of broken crayons. Give your answer in its simplest form.
(a)5/7
(b)2/5
(c)7/12
(d)7/5
4.Square B has vertices (1, 1), (4, 1), (4, 4) and (1, 4). It is rotated 90° clockwise about the origin, and the image is then translated by the vector (2, −1). Work out the coordinates of the image of (4, 1).
(a)(0, −6)
(b)(3, −5)
(c)(1, 3)
(d)(1, −4)
5.A machine produces bolts. In a sample of 250 bolts, 15 are faulty. Work out the relative frequency of a bolt being faulty, giving your answer as a fraction in its simplest form.
(a)50/3
(b)3/47
(c)1/10
(d)3/50
6.Two classes at a school in Coventry sit the same maths test, out of 20 marks. Class A has a mean mark of 14 and a range of 6. Class B has a mean mark of 14 and a range of 14. Write a sentence comparing the two classes, using the mean and the range.
(a)Equal means; Class A is more consistent, smaller range.
(b)Class B did better on average — its range is bigger.
(c)Class A did better on average — its range is smaller.
(d)The classes can't be compared, since the means are equal.
7.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.
(a)8.15 ≤ y < 8.25
(b)8.15 < y < 8.25
(c)8.1 ≤ y < 8.2
(d)8.2 ≤ y < 8.3
8.A company's cost, in £, for producing x items is shown on a graph. The tangent to the curve at x = 50 passes through (30, 400) and (70, 800). Interpret the gradient of this tangent in the context of the company's costs.
(a)The cost decreases by about £10 per extra item
(b)The cost increases by about £400 per extra item
(c)The cost increases by about £0.10 per extra item
(d)The cost increases by about £10 per extra item
9.In a fruit bowl, the ratio of apples to oranges is 5 : 3. Work out what percentage of the fruit in the bowl is apples.
(a)37.5%
(b)62.5%
(c)160%
(d)50%
10.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.
(a)£112
(b)£157
(c)£143
(d)£129
11.Two fair coins are thrown together 400 times. Work out how many of the 400 throws you would expect to give one head and one tail.
(a)100
(b)200
(c)133
(d)300
12.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.
(a)30
(b)15
(c)60
(d)10
13.f(x) = x³ − 3x² − 4. Work out the pair of consecutive integers between which the solution of f(x) = 0 lies.
y = x
(a)4 and 5
(b)2 and 3
(c)0 and 1
(d)3 and 4
14.A conversion graph between kilometres and miles passes through the origin and the point (50, 31), with the number of kilometres on the horizontal axis and the number of miles on the vertical axis. Work out the number of miles equivalent to 1 kilometre.
(a)0.62 miles
(b)1.24 miles
(c)1.61 miles
(d)31.00 miles
15.Which of these statements about solving a triangle is correct?
(a)Two sides + a non-included angle: cosine rule gives the angle directly.
(b)Two sides + angle between them: use the sine rule.
(c)All three sides: use the sine rule for any angle.
(d)Two angles and a side: sine rule finds other sides.
16.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.
(a)£14.50
(b)£13.50
(c)£12.50
(d)£24.50
17.A jug holds 3 litres of a drink that is 60% fruit juice. 1 litre of water is added to the jug. Work out the percentage of the new mixture that is fruit juice.
(a)60%
(b)75%
(c)45%
(d)15%
18.A tank holds 3.2 m³ of water. Work out this volume in litres.
(a)320
(b)32000
(c)3200
(d)3.2
19.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).
(a)(4, 1)
(b)(4, −1)
(c)(−4, 1)
(d)(−4, −1)
20.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?
(a)Line 1
(b)Line 2
(c)Line 4
(d)Line 3

How the 20 questions are shared out

Number — 3 questions (15% of the qualification)
Algebra — 6 questions (30% of the qualification)
Ratio, proportion and rates of change — 4 questions (20% of the qualification)
Geometry and measures — 4 questions (20% of the qualification)
Probability — 2 questions (7.5% of the qualification)
Statistics — 1 question (7.5% of the qualification)

Where an area has fewer printable questions than its share, the shortfall is filled from the other areas. These are original questions, not past papers.